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Патент USA US3088072

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April 30, 1963
A. A. HUDIMAC
3,088,062
ELECTROMECHANICAL VIBRATORY FORCE SUPPRESSOR AND INDICATOR
Filed Feb. 10, 1956
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INVENTOR.
ALBERT A. HUD/MAC
A TTORNEYS
April 30, 1963
A. A. HUDlMAC
3,088,062
ELECTROMECHANICAL VIBRATORY FORCE SUPPRESSOR AND INDICATOR
Filed Feb. 10, 1956
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April 30, 1963
3,088,062
A. A. HUDIMAC
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April 30, 1963
3,088,062
A. A. HUDIMAC
ELECTROMECHANICAL VIBRATORY FORCE SUPPRESSOR AND INDICATOR
Filed Feb. 10, 1956
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INVENTOR.
ALBERT A. HUD/MAC
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ATTORNEYS
April 30, 1963
A. A. HUDIMAC
3,088,062
‘ ELECTROMECI-IANICAL VIBRATORY FORCE SUPPRESSOR AND INDICATOR
Filed Feb. 10, 1956
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INVENTOR.
ALBERTA. HUD/MAC
A TTOR/VEYS
April 30, 1963
3,088,062
A. A. HUDlMAC
' ELECTROMECHANICAL VIBRATORY FORCE SUPPRESSOR AND INDICATOR
7 Sheets-Sheet 6
Filed Feb. 10, 1956
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1_______.______________.___
TO TUNING INDICATOR
A
INVENTOR.
ALBERT A. HUD/MAC
BY
'5 — I”
A TTORNEYS
United States Patent 0
3,@33,0?2
we
IC€
f’a’rerrteel Apr. 39, 1953
2
1
tory force is manifested as the motion of one transducer
part and its backing mass.
3?3§?62
ELECTROMECHANECAL VHBRATORY FORCE
SUPPRESSGR AND lNDlCATQ/“R
Albert A. Hudimac, 2720 Grandview, San Diego, Calif.
Filed Feb. 10, 1956, Ser. No. 564,$35
iii Claims. (till. 318-428)
(Granted under Title 35, US. Code (1952), see. 266)
The external electrical im
pedance, the terminal impedance of the transducer, may
be speci?ed as a function of vibration frequency for a
5 transducer such that there results a combination of me‘
chanical and virtual mechanical elements which in one
case may remain anti-resonant over a broad band of fre
quencies. In a second case, wherein a machine is resili
ently supported from a base, the terminal impedance is
The invention described herein may be manufactured
and used by or for the Government of the United States 10 so speci?ed as to effect a combination of mechanical and
virtual mechanical elements which effectively reduces to
of America for governmental purposes without the pay
zero the dynamic stiffness of the resilient support where
ment of any royalties thereon or therefor.
by protection is afforded to the lowest frequencies Without
This invention relates to the art which deals with vibra
impairing the ability of the resilient support to sustain
tory forces and more particularly to the indication of the
the weight of the machine and withstand shock.
15
characteristics of vibratory forces and the control of
The characteristics of the A.-C. current which flows
vibration of broad frequency ranges and remote adjust
through the transducer and its terminal impedance, and
ment of frequency or frequencies of optimum suppression.
also the velocity of the moving transducer part are di
Motion of practically all types of bodies, machines and
systems is invariably accompanied by vibration and noise.
rectly proportional to the characteristics of the exciting
The desirability of eliminating such vibration and noise 20 vibratory forces which may thus be measured by suitable
current or velocity indicators.
has long been recognized and much effort has been di
Accordingly, it is an object of this invention to suppress
rected toward the solution or" this problem. The problem
vibration.
is of particular gravity in submarine warfare where a ves
Another object of this invention is the reduction of
sel’s safety may depend upon the suppression of vibra
tion and noise of the auxiliary equipment which is nor 25 radiated and self noise of a sea-going vessel caused by
transmission of vibration of machines to the hull of the
mally left in operation in ultra-quiet or patrol-quiet con
vessel or the passage of the vessel through the Water.
ditions.
Still another object of this invention is the protection
Mechanical anti-resonant systems comprising springs
of
sensitive or fragile equipment from vibration or shock
and masses have been added at suitable places in a vi
bratable mechanical system to produce a large mechani 30 transmitted from its base.
A further object of this invention is the suppression of
cal impedance at the frequency of anti-resonance of the
vibration
over board frequency ranges.
added elements. Such an arrangement is effective only
Another object of this invention is the remote control
over a narrow ‘band of frequencies unless it is damped,
of the frequency or frequencies of optimum vibration
in which case its effectiveness at resonant frequency is re
duced. Further, the resonant frequency is ?xed or at 35 suppression.
least ‘difficult to adjust. Adjustment cannot be effected
remotely.
Another known solution is the interposition of resilient
means between the element to be protected from vibra
tion and the mechanical element in which the vibration
produced force is generated or through which it is trans
mitted. To work effectively the impedance of such resili
ent means must be small compared to the impedance of
Still another ‘object of this invention is the reduction
of the dynamic stiffness of a resilient support without
impairing the ability of the support to sustain a load and
absorb shock.
A further object of this invention is to maintain the
mechanical impedance of a vibratable mechanical system
at an extremely high value over a broad frequency range.
Still another object of this invention is to maintain a
the protected element or of the vibration transmitting 45 low impedance motion transmitting path in a vibrata-ble
mechanical system down to as low a frequency as is de
element. This requires either springs which are too soft
sired.
to support the protected machine or the restriction to
A further object of this invention is the provision of
high frequencies.
a vibration suppressor having a structure which is sub
The present invention is composed of electrical and
stantially independent of the physical characteristics of
mechanical elements having speci?ed properties and em
the system in which vibration is to be suppressed.
bodied in a design such that the electrical elements are
Another object of this invention is to measure vibra
transduced into virtual mechanical elements. Certain of
tory forces.
the electrical elements may be remotely located and ad
Still another object of this invention is to indicate the
justable to effect remote adjustment of virtual mechanical
impedance thereof. Further, the electrical elements may 55 imbalance of a dynamic machine.
Other objects and many of the attendant advantages
be designed to provide electrical impedance which varies
of this invention will be readily appreciated as the same
with frequency variations of the exciting vibratory forces
becomes better understood by reference to the following
in such a manner as to maintain over a broad frequency
detailed description when considered in connection with
band a virtual mechanical impedance in the system which
will produce optimum vibration suppression. More spe 60 the accompanying drawings wherein:
FIGS. 1a and 1b show one form of the invention as
ci?cally the invention comprises an electro-mechanical
transducer which senses the force tending to create vibra
tion of a machine or the base on which the machine is
mounted. This exciting force is manifested as a voltage
applied for the purpose of suppressing vibration of a
noisy machine rigidly mounted on a base and the equiva
lent mechanical circuit thereof;
FIG. 2 is a sectional view of the transducer of FIG. 1a;
generated by relative motion of two transducer parts 65
FIG. 3 is a sectional view of part of the structure of
which causes a current to flow in a circuit including the
transducer and an external electrical impedance. The
FIG. 2;
FIG. 4 is a circuit diagram of the electrical connec
external impedance adjusts the phase and amplitude of
of the current in such a manner as to cause this current
tions of the transducer of FIG. 2;
FIG. 5 is a modi?cation of FIG. 4;
70
posite to the exciting forces. Where neither the machine
FIGS. 6a and 6b show another form of the invention
nor its base is permitted to move transmission of the
‘as applied for the purpose of isolating an object resiliently
to create forces in the transducer which are equal and op
exciting energy to the system is prevented and the vibra
3,088,062
3
41.
equal and opposite to the exciting forces tending to pro
duce the vibration. In effect, the transducer, when
properly terminated, presents an exceedingly great im
pedance to the vibratory exciting forces and, furthermore,
mounted on a noisy base and the equivalent mechanical
circuit thereof;
,
FIGS. 7a—1lb inclusive show several additional forms
of the invention as applied and the respective equivalent
mechanical circuit diagrams thereof;
FIG. 12 diagrammatically depicts the manner in which
will do so over as Wide a frequency band as the terminal
impedance corresponds to that speci?ed below.
a number of transducers of this invention may be ar
ranged to suppress vibration in three linear and three ro
Analysis
tational directions;
The condition on the electrical termination is obtained
FIG. 13 is a schematic diagram of one circuit which 10 by treating the linearized form for steady state harmonic
provides a terminal impedance of the type speci?ed;
oscillation. More complicated behavior can be obtained
FIG. 14 is a schematic diagram of the invention modi
by superposition of these results.
?ed for use as an indicator of vibratory forces;
The D.-C. current flowing through the coils of the trans
FIG. 15 shows another manner in which the inven
ducer produces a flux, (#1, in the cores 16, 18 which can
tion may be used as an indicator of vibratory forces;
15 be expressed as
FIGS. 16 and 17 graphically indicate results obtainable
¢1=¢10+(a¢1/ag)Ag
(1)
with this invention; and
provided the change in gap or incremental gap Width, Ag,
FIG. 18 graphically indicates one type of optimum ter
is small compared to the undisplaced gap, g0. Here on
mination.
In the drawings like reference characters refer to like 20 is the flux at equilibrium position and 6¢1/8g is slope of
curve ¢1(g) at the equilibrium position. Thus, ¢1 has
parts.
a static component and an A.-C. component. There is
As shown in FIG. la, a machine 10’ Which is “noisy”
an additional A.-C. ?ux, 452, which is caused by the A.-C.
or vibrates due to dynamic imbalance or other factors is
current, ib circulating in the coils due to relative motion
rigidly secured to a base 12 which may be, for example,
of the two transducer parts. It is given by
the hull plate of a vessel or a structural member secured
thereto.
In this case the source of noise might alterna
tively be in the base and caused by vibration of other
machines or passage of the vessel through the water.
The vibration suppressor 14 comprises a variable reluc
tance transducer having two U-shaped cores 16, 18
25
The ?ux creates a force of traction on the pole faces of
the cores, given by
(FIGS. 2, 3) of oriented grain ferromagnetic material,
each wound with a number of turns of conductive wire
20, mounted in cups 22, 24, and impregnated with potting
compound 26 which rigidi?es each core, coil and cup
where A is area of each pole face, and where factor of
2 is used because there are two gaps.
We shall assume
assembly. Cup 24 is rigidly secured to base 12 while 35 that ¢1>>¢2. Then substituting from Equations 1 and 2
cup 22 is rigidly secured to a resilient circular plate 28‘
into 3, and neglecting second order, D.~C. and second
which may be a stainless steel leaf spring rigidly mounted
harmonic terms, we get
to base 12 by means of symmetrically arranged studs 30
or the like and ?xedly carrying a backing mass or weight
32. Terminals 34 are provided for electrical connection 40
of the coils 20.
p
‘The coils 20 of cores 16, 18 are connected in series
This force represents a tension on or attraction between
‘each pair of pole faces. Hence, the coe?‘icient of Ag/Z
aiding and excited with a D.-C. currentfed from battery
1n the first term on the right represents a pseudo stiffness,
36 (FIG. 4) through variable resistor 38 and a parallel
s’. Because all terms except apl/ag are positive, the co
tuned circuit comprising capacitor 40 and inductance 42. 45 efficient
The tuned circuit, tuned to vibration frequency, is used
to prevent shorting through battery 36 of the A.-'C. volt-j
age generated in the coils during operation of the vibra
[4510f 5451/59)
7rA
tion suppressor while a voltage across resistor 38 is con
herein designated as s’ represents a negative stiffness. A
veniently used to supply a tuning indicator ‘(not shown).
50 real spring with stiffness s>s' is necessary to maintain a
The described circuit provides a DC. magnetic bias.
stable undisplaced gap go. The total tension on each
core then is
The series connected coils 20 are electrically terminated
into a variable electrical impedance 44 to be described
hereinafter.
An alternative arrangement shown in FIG. 5 shunts 55
the A.-C. voltage of coils 20 across battery 36' by means
The force FT is balanced at each core by forces or
of capacitor 46 and the coils are coupled with the ter
reactions peculiar to that core. At the core ‘13 fastened
minal impedance 44’ through a transformer 48. In both
to the base, the force FT is balanced against the open
arrangements the magnetic bias may be alternatively pro
circuit force of the machine, FF , and the reaction or inertia
vided by permanent polarization of the cores, thus elimi
due to the internal mechanical impedance of the machine,
nating the D.-C. source and tuned rejection ?lter or the
Z1, and to the mechanical impedance of the base and parts
latter may be made broad band.
?xed'thereto, zb. The open circuit force of the machine
The described transducer performs two functions si
is the force the vibrating machine would exert on an
multaneously. First it “senses” the exciting vibratory
in?nitely rigid’foundation. Hence,
forces which tend to create vibration of the base 12 and, 65
machine 10 and which are manifested as relative motion
FT=_vb(Zi+Zb)+5E
(6)
of the two parts of the transducer and an A.-C. voltage
where vb is the velocity of the base and of the machine
generated thereby. This voltage ‘produces an A.-C. cur
and the positive sense of g, vb (and later, of v,,) being
rent which flows in a loop through the transducer coils
taken from the transducer toward the base. In core 16,
and through the external electrical impedance. The ex 70 the force of PT is balanced by the reaction due to the
ternal electrical impedance adjusts the magnitude and
mechanical impedance of the core and the mechanical
phase of the current. The second function is the trans
lmpedance z,, of its backing mass 32. Hence,
duction of the adjusted current into suppressing forces
whereby the transducer creates forces (and applies them
to the vibrata'ble body, the base and machine) which are
FTzvazb
where Iva is the velocity of mass 32 and core 16.
(7)
8,088,062
5.
6
In this case z, can be considered as impedance of a ma
1 The change in flux, caused by change in gap and by the
be induced; it is given by
chine, which replaces the backing mass and is to be pro
tected from forces transmitted through the base. Since G
is a positive number, it is necessary for either case that
‘Where E is in volts, ¢ is in gauss, and N is the number
of turns on the cores. Substitution from Equations 1
(Ze+ZT) be purely reactive. This requires that the
transducer and terminating impedance be lossless. The
case of lossy elements will be considered below. It
should be emphasized that vibration suppression of base
circulating current in the transducer, causes a voltage to
or of the backing mass is obtained for as wide a band
10 of frequencies as Equations 12 or 13, respectively, hold.
Further insight can be obtained into the conditions for
the suppression of oscillations by considering the equiva
lent mechanical circuit of FIG. 1b. Only the case forv
the suppression of the vibration of the base is given here.
neglected. Note that E is taken positive in same direction
as ib. Completing the circuit with load Ze, the voltage 15 The case for suppression of vibration of the backing mass
or an isolated object substituted therefor is very similar.
drop across the load being equal to the induced voltage,
Solving simultaneous Equations 11 for vb gives
where terms of second order or of second harmonic are
E=Zeib
(10)
where Ze is the impedance of the electrical termination
20
44 or 44' of the transducer.
The coef?cient of (—]'wib) in Equation 9 is the self
inductance of the transducer. An actual transducer will
also have an A.-C. resistance, RT, due to windings, eddy
currents and hysteresis, and also distributed capacitance.
For this reason the coet?cient is replaced by ZT, the 25
The total impedance, z into which the “open circuit force”
blocked electrical impedance of the transducer. The
blocked impedance may be de?ned as the impedance with
drives is
both A.-C. rand D.-C. current ?owing and the gap held
(ZT+ZG)ZJ
?xed.
I
~s1
zT= jw41rNz(l9-§0i4) +RT
( 10a)
(15)
We now have three simultaneous Equations in 6, 7,
and 10. The desired independent variables are va, vb and
i,,. We therefore express
Q¥—
_.
-
_g?:?Q
dt -2(11b 0,), Ag--
jw
(5T+Ze)[_j£§_:—s/)+Zn]'i‘G
30
Note that if the denominator of the last term is Zero, i.e.,
tzi~+ze>[—j(i?ll+ai+e=o
(11)
then z is in?nite.
(12)
Since 3’ is ?nite, W1, must be zero, as
was demonstrated in the previous paragraph. Equation
Equations 6, 7, 4, 10 then become:
15 can be rewritten
45 Clearly, z is composed of three impedances in series:
Z1, zb and a parallel combination with an impedance
of za in one branch, and in the other a series arrangement
of impedance
50
Equations 11a, 11b and 110 can be written
anaizaia i
as shown in the equivalent circuit of FIG. lb. It will be
O
noted that the condition given by Equation 12 is the condi
llziazzazs 11b = 35
tion that the parallel element is anti-resonant. Stated
55
(13111321133 vs
0
otherwise, the condition that vb=zero is satis?ed by mak
ing the mechanical reactance za equal and opposite to
The condition that vb be zero is that the complementary
the mechanical reactance
60
G/ZTHH;
(J)
The impedance of the parallel branch in FIG. 1b is in
?nite at anti-resonance if the elements are not lossy.
provided that the determinant of the matrix is not Zero.
practice, this is not possible.
G. a positive number, is herein termed the electrome
chanical coupling constant. The impedance
J
In
Let
65
where R=the resistance RT of the actual transducer plus
the real component of Z2 and X =the reactive components
of Z; and Ze. Then,
(0
is herein de?ned as the effective mechanical capacitative
G
L
.G
GR
impedance of the transducer, conveniently designated as 70
Z,+ZT*_JX+F
(17)
XCT. In like manner, the condition that va be zero is
that the complementary minor of (123 be zero, i.e.,
provided, as is reasonable, that X>>R. Now the resist
ance of the parallel circuit at anti-resonance, Rar is
g0
(13)
75
[2312
(18)
1
3,088,062
p
'
0‘
I
Under the condition that X>>R,
GR;
GR
a
through D.-C. blocking capacitor 78, is connected to the
_@ a _.(s+s’) 2
TFWZTJFZJFG‘“ j w
where use of condition (12) was made.
_-_
Glad"
Rar—‘-—_———,%
R amps-A 2
other end of coils 20.
It has been shown that the desired external impedance
(19)
G
Hence,
(20)
where za=jwMw the impedance of mass 32. Since both
terms on the right are the negative of real impedances, it
and Equation 16 becomes
10 is clear that Ze is a negative impedance.
An important class of negative impedance is obtained
Z=Zi+Zb+Rar
(21)
by employing positive feedback in an ampli?er. A species
Thus, it is seen that in order to make Rar large, Z8 and G
of this class is the series type shown in FIG. 13 which is
OJ
should be large, R should be as small as possible and
so connected that the current i ?owing through the circuit
15 (and through coils 20‘) as a whole ?ows through the ampli
?er input 49 in series with the ampli?er output. The
phases are such (with an even number of stages) that the
should be small. This last requirement implies that the
resonant frequency of the transducer, f,,,, be near the fre
ampli?er output tends to increase the current i, and thus
quency range in which suppression is desired. It can be
shown that these conditions also result in a small circulat
ing current, ib, and velocity v,,. This is desirable because
to retain linear operation 2}, must be a small fraction of
the D.-C. bias current and the displacement must be a
small fraction of go. Furthermore, since R=RT plus the 25
real component of Ze, R becomes small and RM large
when RZe is negative and approaches RT in magnitude.
positive feedback is realized. The negative feedback
within the ampli?er 60 effected by elements 70, 72, en
sures stability of the total negative impedance.
If the ampli?er have a gain A and output impedance R,
and the voltage applied across terminals 74, 76 be E, the
summation of voltages around the series loop gives
E=iZ3+iR1—iAZ3
(22)
where Z3 is the impedance of the input 49. Thus,
It is apparent that the electrical impedances speci?ed
above require the use of negative inductances and/ or nega
E/z'=Ze=Z3(1—A)+R1
tive capacitances in order to provide impedances which
vary with frequency in accordance with Equation 12 or
If A is greater than one the ?rst term on the right is a
13.
negative impedance. To determine the value of this nega
tive impedance Z3, for given parameters A and R1, it is
only necessary to equate the values of Z,a from Equation
Such elements do not exist in nature but circuits us
ing negative resistance do exist for obtaining such ele
ments.
Such circuits are discussed on page 187 of B'ode’s
“Network Analysis and Feedback Design,” published in
1951 by Van Nostrand. Negative resistance has been
(23)
12 and 23
'
35
thoroughly studied and a number of such well known cir
cuits are described E. W. Harold in “Negative Resistance
and Devices for Obtaining It,” Proc. I.R.E., vol. 23, No.
=10, October 1935, page 1201.
40
However, it will be readily appreciated that the inven
where L=G/s+s' and C=Ma/G. From Equation 25 it
tion described herein will eifectively suppress vibration in
is seen that the circuit whose impedance is Z3 comprises
a narrow frequency band When the transducer is electrical
the elements shown within the dotted box 49 where re
ly terminated in a real, ?xed impedance component which
sistor 50 has a value RT/A~1, resistor 52 is R1/A--1, in
has a value determined in accordance with the stated de
sign criteria at the particular frequency of interest. Fur 4:5 ductor 54 is LT/A—1, capacitor 56 is C/A-l and in
z3-A——_1[R1+RT+JwLT+ “Maj/m0 ] (25>
ductor 58 is L/A'-—-1.
Thus the circuit of FIG. 13 having components as spec
i?ed above comprises an impedance into which the trans
suppression. The value of G can also be controlled re
ducer may be terminated in order to effect optimum sup
motely. Thus, for example, the vibration suppressor of
this invention may be arranged to effect optimum sup 50 pression over a band of vibration frequencies of several
octaves. With such termination the transducer of this
pression at one predetermined vibration frequency. If
invention in addition to its primary function of steady
such frequency should for some reason vary from such
state vibration or noise suppression, will largely prevent
predetermined frequency the physical arrangement or
motion of the base and machine due to shock or impulsive
structure of the suppressor need not be changed. It is
merely necessary to change the value of the terminal im 55 noise. This is true ‘by reason of the fact that shock
comprises a broad band of vibration frequencies. When
pedance, which may be a variable capacitor or inductance,
at a remote location or to change the value of G by, for
Z8 is such that broad band suppression is provided, then
example, changing the magnetic bias.
that portion of the shock induced motion which is due
Since broad band vibration suppression is to be desired
to those vibration frequencies within the broad suppres
in many instances the terminal impedance 44 or 44' may 60 sion band is eliminated. In other words, the broad band
take the form shown in the circuit of FIG. 13 which pro
vibration suppressor of this invention is also a “shock
absorber.”
vides over a broad band an impedance Ze, looking from
the transducer coils, of the nature speci?ed in Equations
It is to be understood that the circuit of FIG. '13 is
12, 13.
but one exemplary embodiment of a terminal impedance
A series connected impedance 49 comprising resistors 65 which can meet the speci?ed conditions for a wide fre
50, 52, inductance 54 and capacitor inductor tank 56, 58 is
quency range. Numerous other circuit arrangements
connected to provide the input to a stable, even stage am
which satisfy the conditions for terminal impedance may
pli?er 64} (shown with two stages) comprising an electron
be produced in accordance with the stated principles.
discharge tube 62 (such as an ordinary vacuum triode)
The curves of FIG. 16 indicate exemplary comparative
resistance capacitance coupled through elements 64, 66 to 70 results which are obtainable with the vibration suppressor
electron discharge tube 68. A negative feedback circuit
of this invention. To obtain these curves the structure
comprising resistor 70 and capactior 72 couples the plate
and circuitry of FIGS. 1a and 4 are employed with a
of tube 68 to the cathode of tube 612. Terminal 74 is
mechanical shaker unit substituted for the noisy machine
connected to one end of the series aiding transducer coils
10 and a velocity detector is secured to base 12. Curve A
230 while terminal 76, connected to the plate of tube 68 75 represents the values obtained with the transducer un
thermore, the value of this terminal impedance can be con
trolled remotely in order to vary the frequency of optimum
3,088,062
terminated (Ze==in?nity) but bias current ?owing and
curve B represents values obtained with an optimum
10
low impedance path or mechanical “short circuit” is pro
vided across impedance z,,. Such a low impedance path
termination (for the resonant frequency of the system)
is provided by series resonance in the shunt path which
determined in accordance with the criteria stated above.
The parallel LC circuit lid, 42 is tuned to the center of
the band of frequencies used. As indicated in FIG. .16
occurs when the reactance
a relative velocity suppression of ‘26 decibels is obtained
at resonant frequency with the optimum termination, a
J
0)
equals reactance G/Ze+ZT. Thus, isolation is obtained
when
capacitor of 1.9 microfarads. There is a net suppression
I
of vibration over a band Width which is 11 percent of 10
z.= - zi+ GHQ-EL)
central frequency while there is an increase in velocity
of vibration outside of this band width with a constant
The action of this type of suppressor may be explained
electrical terminal impedance.
as follows: The vibratory exciting force tends to vibrate
At frequencies far removed from the resonant fre
object 80 by exerting a force through real springs 82.
quency only a few db in vibration supprwsion were ob 15 When a force is exerted across the springs there is rela
tained. The reason can be seen with the aid of Equa
tive motion between the two transducer parts which in
tion 21. The quantity (Z1+Zb) is very large off reso
duces a voltage in the coils thereof. Thus a current is
nance, while R8,r at best is of the same order. This re
caused to flow through the coils and the terminal imped
sult demonstrates the need for careful application of the
ance (not shown in FIG. 6a). If the termination is as
design criteria discussed below Equation 2.1 if good vibra 20 speci?ed the resulting current has just the proper magni
tion suppression is to be achieved.
It is to be under
stood that while the curves of FIG. 16 corroborate the
results indicated by the equations set forth above they
are merely indicative of results obtainable with a single
tude and phase as to cause a force to be exerted by the
core attached to the object 80 (and of course on the
other core) which will exactly cancel the force of the
springs on the object. The object thus has zero net force
transducer in a limited situation and are not intended 25 acting upon it and so remains stationary. It will be seen
to limit in any way the scope of the application of this
that the arrangement of FIG. 6a with the speci?ed ter
invention to other situations.
mination effectively reduces, and even entirely removes
Good vibration suppression is obtained at frequencies
over a wide band of frequencies, the dynamic stiffness
other than resonant frequencies. FIG. 17 shows the
of springs '82 which support object '80. However, the
relation between relative suppression of vibration velocity
ability of the springs to support a heavy object and to
and frequency in a single case. The plot shows that vi
withstand shock remains unimpaired.
bration suppression is best at resonant frequencies where
In the arrangement of FIG. 6a, a lossy transducer does
(z1+zb) is small, that suppression increases at the reso
not prevent reduction of the dynamic stiffness to Zero but
nant frequency, ;f,, of the transducer, and that it is sig
does replace such stiffness with a resistance Rs given ap
ni?cant throughout the frequency band, from 100v to 350 35 proximately by
cycles per second.
FIG. 18 shows the relation between values of the ter
minating capacitor for optimum vibration suppression and
R,= R/G(S ‘of >
frequency for the single case of FIG. 17. The two ter
and thus it is seen that G should be large and R small
minal network of FIG. 13 may substantially fit this curve 40 to make Rs small.
and thus the vibration suppression indicated in FIG. 17
‘From FIG. 612 it can be seen that vibration of the base
may be achieved over a wide band of frequencies. The
84, and of any device rigidly secured thereto is prevented
curve of FIG. 18 is the value of a terminating capacitor
when vb is zero, a condition which occurs when an in?nite
calculated from Equation 12 and from measured values
impedance is provided by anti~resonance of the parallel
45 tank circuit. Therefore, the terminal impedance is speci
of G and ZT for a particular transducer.
An investigation of the conditions of electrical termina
?ed by equating za to the sum of G/Ze+ZT and
tion of Equations l2, l3 reveals that the terminal imped
ance Z6 is speci?ed solely as a function of the physical
and electrical structure of the transducer and vibration
frequency. There is no relation between Z8 and the phy
Of course, with such termination, object 80 will vibrate.
The structure and arrangement of the system shown in
sical characteristics of the machine and base, the system
in ‘which vibration is suppressed, providing only that the
FIG. 7a is the same as that of FIG. 6a but in the former
change in gap width remain small. Thus, one vibration
the source of noise is object 80 which may be a noisy
suppressor of this invention may be applied with equal
machine. The equivalent mechanical circuit of the sys
effectiveness to different mechanical systems with no 55 tem of FIG. 7a, shown in FIG. 7b, is substantially
change of the suppressor required. Large variations in
similar to that of FIG. 6b and '3’ still represents the ex
amplitude of vibratory forces can be accommodated, for
citing vibratory force which is now the open circuit force
example, by varying the mass of weight 32.
of the machine 80. The position of the impedances repre
In the embodiment shown in FIG. 6a an object 180 to
senting base and machine or object are interchanged in
be isolated from vibration ‘and shock is mounted through 60 the equivalent circuit. Where the noisy machine is to be
springs 82 on base “84 from or through which vibration
prevented from vibrating the terminal impedance is speci
and shock are transmitted. The two transducer parts
?ed by
which may be identical to elements ‘16 through 26 of
FIG. 2 and having the same electrical connections and
circuitry of FIGS. 4 or 5 are respectively rigidly secured 65
Where transmission of vibration to the base is to be
to object 80 and base ‘84. From the equivalent mechani
prevented the terminal impedance is speci?ed by
cal circuit of ‘FIG. 6b, where 3? is the open circuit force
of the noisy base, zb is the impedance of the base 84, 1a
is the impedance of object 80, s is the stiffness of springs
to
82, s’ is the negative stiffness of the transducer and
As shown in FIG. 8a and 921, the arrangement of ‘FIG.
G/ZQ-I-ZT is an impedance introduced by the terminated
1:: can be utilized with a noisy machine ‘86 supported by
transducer as speci?ed above, the operation of the sys
springs 88 on a base 90 with the suppressor mounted on
tem can be readily determined. For the desired condi
either the machine (FIG. 8) or base (FIG. 9). In the
tion of isolation of object 80, the velocity va thereof
must be zero. This condition therefore obtains when a 75 mechanical equivalent'circuits of FIGS. 8b and 9b, Z1 is
11
3,088,062
the impedance of the machine 86, zEL is the impedance of
mass 32, s is the stiffness of leaf spring 28 and sm is the
12;
rotational exicting force and the phase and magnitude
of the resultant linear suppressor forces are opposite and
stiffness of springs 38. In either case the termination is
the same as that speci?ed in Equation 12. With this ter
mination it will be seen that an in?nite impedance is pre
sented to the existing force when the transducer is
mounted on the machine since the parallel tank circuit is
equal to the exciting force in the one linear mode. Pair
14A would suppress linear vibration parallel to the X
axis of FIG. 12 and rotational vibration about the Z azis.
yPair 14B would suppress linear vibration parallel to the
anti-resonant (FIG. 8b). Therefore, vibration of both
machine 86 and base 9%)‘ is prevented.
larly, pair 14C would suppress linear vibration parallel
in series with the in?nite impedance of the tank circuit
shown in FIG. 12 may be selected to suppress any sub
combination of the possible vibrational modes.
In recapitulation, it may be stated that the vibration
suppressor described herein performs the fundamentally
desired function of providing a vibratable mechanical
system with an effective mechanical impedance which
Z axis and rotational vibration about the Y axis. Simi
to the Y axis and rotational vibration about the X axis.
With the transducer mounted on the base the latter is 10 Obviously a suitable subcombination of the transducers
while velocity of the machine is shunted across the base
by springs 88. Therefore the base remains still and the
machine behaves as if the springs 88‘ were mounted on
an in?nitely rigid base.
The arrangements of FIGS. 10a and 11a are respec
tively the same as those of FIGS. 8a and 9a but the
source of noise in the former is in the base. The termi
nation remains as speci?ed in Equation 12. With the
transducer attached to the machine (FIGS. 10a, 10b)
an in?ite impedance is presented by the tank circuit to
velocity of the machine while velocity of the base is
shunted across the machine by springs 88. Here the base
may vibrate but the machine is still. With the trans
ducer attached to the noisy base (FIGS. 11a, 11b) an
in?ite impedance is presented to the exciting vibratory
force by the anti-resonant tank circuit. Thus, as in the
arrangement of FIG. 8a and of FIG. 1a vibration of both
the machine and base is prevented by reason of the fact
that no transfer of energy of the exciting force to the
suppressed system is possible.
While the analysis and description which appears above
has been con?ned to a vibration suppressor embodying
a variable reluctance transducer it will be readily appre
ciated that the principles of the invention are equally ap
plicable to other types of electromechanical transducers.
For example, in the case of the moving coil type of trans
ducer where the moving coil is used in place of one core
may be maintained at an optimum value over a broad
frequency range and may be remotely adjusted. De
pending upon the particular system and the results de
sired this function is performed in one of two ways. In
one case there is provided in the system an extremely
high mechanical impedance which prevents transfer of
energy. Alternatively, there is provided an extremely low
impedance series resonant motion transmitting path, down
to frequencies as low as desired, which shunts the velocity
of a part in which vibration is to be prevented.
Measurement of Vibration
As will be shown below each of the quantities ib, the
adjusted A.-C. current ?owing through the transducer
coils and the terminal impedance, and 11,, the velocity of
one moving transducer part is directly proportional to the
exciting vibratory force and the suppressor forces created
by the transducer. Therefore, to measure the magnitude
of the exciting force it is merely necessary to measure this
current or velocity. Thus, to measure the open circuit
‘force, or imbalance of machine 10 of FIG. 1a, it is merely
necessary to provide a suitable current indicating device
and the ?eld structure in place of the other it can be
such as the ammeter 100 shown in FIG. 14 in the trans
demonstrated that the results are the same as for the 40 ducer coil circuit. Alternatively, as shown in FIG. 15, a
variable reluctance transducer, except that the negative
stiifness thereof, s’, is zero and the electromechanical
coupling constant G is de?ned as
G=B2l2>< 10*9
where B is ?ux density in the gap occupied by the moving
conventional velocity detector 102, well known in the art,
may be mounted on the moving transducer part or the
mass 32 ?xed thereto. The reading of detector 102 or
amrneter ‘100 is directly proportional to the exciting force
45 and the indicators may be so calibrated as to yield direct
measurements of the unknown forces. It is to be under
coil and l is total length of Wire of the moving coil in
stood that FIGS. 14 ‘and 15 show circuits and structures
the magnetic ?eld.
which may be identical with those of FIGS. 4 and 1a re
Similar analyses using lumped parameters could be
spectively save for the addition of elements 100 and 102.
made for still other types such as electrostatic, tangen 50
As will be readily ‘appreciated each of the embodiments
tial variable reluctance and tangential electrostatic. A
or ‘applications described herein may be modi?ed by addi—
somewhat more complicated device using magnetostric
tion of either ‘a current or velocity detector, or both, to
'tive or piezoelectric transducers could be used. In these
provide apparatus for measuring vibratory forces. It will
types the generated ‘forces, mass and stiffness are not
be seen that in addition to the linear relation between
lumped and hence analysis is more complicated, but the 55 magnitude of exciting forces and either current or velocity,
basic principles still apply.
there is a linear relation between the frequencies and
In the discussion thus far, the forces treated have been
phases thereof and these characteristics of the exciting
unidirectional linear oscillations and they tend to give
forces may be measured by measuring frequency and
rise to unidirectional displacements. In the general case
phase of current or velocity. For example, the ammeter
of a rigid machine, there can be three mutually perpen 60 100 may be replaced with ‘a suitable frequency or phase
dicular components of linear Vibration ‘and three mutually
detector or the latter may be provided in addition to the
perpendicular components of rotational vibration. To
ammeter1
suppress vall such components would require six of the
Analysis
described suppressors 14, as diagrammatically illustrated
in FIG. 12, which are arranged in three pairs, 114A, 14B, 65 When the external electrical termination of the trans
and 14C with the pairs A, B, C being oriented mutually
ducer is chosen so as to suppress vibration of the base, the
perpendicular to each other. Thus the transducers of
open circuit force, 3? is effectively transferred to the total
one pair, with axes of vibration (or linear vibration sup
backing mass. This can be seen by noting that, when
the velocity of the base is zero, the forces produced by the
would take care of ‘one linear and one rotational mode of 70 transducer cancel the force in the machine. This bucking
vibration, when the magnitude, phase and points of ap
force is obtained in part from the traction on the base
plication of the suppressor forces created by the trans
‘core and‘ in part due to the strain on the (dynamic)
ducers of such pair are such that the moment of force
spring. The traction on the backing mass core is equal
exerted by the pair of suppressor forces is equal to the
and opposite to that on the base core; the reaction of the
rotational moment of the particular mode of vibratory 75 (dynamic) spring on the backing mass is opposite to its
pression) parallel and separated by a suitable distance
3,088,062
13
14
said transducer remains high over a broad band of fre
reaction on the base. Hence the forces exerted on the
total backing mass are opposite to the bucking forces.
quencies.
3. The structure of claim 1 wherein said circuit means
Since the bucking forces are equal and opposite to the
open-circuit force of the machine, the force on the backing
mass is equal to the open~circuit force.
includes means for varying said electrical impedance with
frequency in accordance with the tendency of said
mechanical impedance to vary with the frequency where
This can be proved rigorously by solving Equations
11a, 11b, 1110 for v9‘ and then imposing the condition for
vb-_—‘0, i.e., Equation 12. The result is
by the mechanical impedance of said transducer remains
high over a broad band of frequencies.
4. A transducer comprising a pair of cores of magnetic
10 material, a coil on each core, spring means resiliently
interconnecting said cores, means for energizing said coils
Clearly, then, if the total backing mass is known, and
if v9, ‘for the condition vb=0 is known, 3“ is given by the
product of these two values, i.e.
in series aiding to provide a steady magnetic bias, and
electrical circuit means connected with said coils for pro
viding said transducer with a low effective mechanical
15
When the external electrical termination of the trans
impedance.
5. The structure of claim 4 wherein said circuit means
includes means for providing a negative electrical imped
ducer is chosen so as to suppress the vibration of the base,
ance in said circuit.
6. The structure of claim 4 including means in said
transducer and the external electrical termination is of
such a magnitude and phase that it creates a force in the 20 circuit for varying the electrical impedance thereof in
accordance with the tendency of said mechanical imped
transducer to buck out the open circuit force.
ance
to vary with frequency.
If Equations 11a, 11b, ‘and 110 are solved for ib and
7. A transducer comprising a pair of cores of magnetic
then the condition for vb=0 are imposed (i.e., Equation
material, a coil on each core, spring means resiliently
12), the result is
interconnecting said cores, means for energizing said coils
the current circulation through the loop formed .by the
,-b =5cZZL><_1.Qi?¢_I/9l
( Ze+ ZT ) Zn
25 in series aiding to produce a steady magnetic bias, and
electrical circuit means connected with said coils, said
circuit means having an electrical impedance which e?ec
But by Equation 12
tively provides said transducer with a high mechanical
30
35
All of the quantities in the denominator on the right
hand side can be determined. The current, ib, can be
determined by measuring the voltage drop across a small
resistor placed in series with the external electrical ter—
mination such as the ammeter of FIG. 14.
Note that the machine vibration of which is to be meas
ured need not be placed on any particular test mount.
impedance, said circuit means including means for indi
cating the current therein.
8. A transducer comprising a pair of cores of magnetic
material, a coil on each core, spring means resiliently
interconnecting said cores, means for energizing said coils
in series aiding to produce a steady magnetic bias, elec
trical circuit means connected with said coils, said circuit
means having an electrical impedance which effectively
provides said transducer with a high mechanical imped
ance, and means for indicating the relative velocity of said
cores.
9. The structure of claim 7 wherein said circuit means
includes means for varying said electrical impedance with
frequency in accordance with the tendency of said
mechanical impedance to vary with the frequency where
45 by the mechanical impedance of said transducer remains
high over a broad band of frequencies.
10. The structure of claim 8 wherein said circuit means
includes means for varying said electrical impedance with
Speci?cally, it can he “in situ,” i.e., in the place that the
frequency in accordance with the tendency of said
machine is actually used.
Obviously many modi?cations and variations of the 50 mechanical impedance to vary with the frequency where
by the mechanical impedance of said transducer remains
present invention are possible in the light of the above
high over a broad band of frequencies.
teachings. It is therefore to be understood that within
the scope of the ‘appended claims the invention may be
References Cited in the ?le of this patent
practiced otherwise than as speci?cally described.
What is claimed is:
UNITED STATES PATENTS
55
l. A transducer comprising a pair of cores of magnetic
material, a coil on each core, spring means resiliently
interconnecting said cores, means for energizing said coils
in series aiding to produce a steady magnetic bias, and
electrical circuit means connected with said coils, said
circuit means having an electrical impedance which once
t-ively provides said transducer with a high mechanical
impedance.
2. The structure of claim 1 wherein said electrical
impedance is a negative impedance determined in accord 65
ance with the characteristics of the transducer and varies
with frequency whereby the mechanical impedance of
1,535,527
1,535,538
1,997,423
2,136,219
2,226,571
2,302,219
2,484,022
Harrison _____________ __ Apr. 28,
Max?eld _____________ __ Apr. 28,
Loser _________________ __ Apr. 9,
Scherbatskoy __________ __ Nov. 8,
McG-oldrick __________ __ Dec. 31,
Hostetler ____________ __ Nov. 17,
Esval ________________ __ Oct. 11,
1925
1925
1935
1938
1940
1942
1949
2,660,062
Frowe _______________ __ Nov. 24, 1953
2,722,194
2,776,560
2,788,457
Hoffman ______________ __ Nov. 1, 1955
Erath _________________ __ Jan. 8, 1957
Griest ________________ __ Apr. 9, 1957
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